Math Tutoring on Graphing Rational Functions
Functions are given by the quotient, or ratio, of two polynomials, are called rational functions. Notice there is a numerator and denominator, and both the numerator and denominator are polynomial functions. The domain of a rational function is restrictive to those x values that do not result in division by zero. Remember, we are not allowed to have zero in the denominator of a fraction. To determine the domain of a rational function, we will set the denominator equal to zero and solve. The graphs of rational functions can be rather complicated to a graph. First, we find the intercepts if there are any. Then we find the vertical asymptotes by setting the denominator equal to zero and solving. However, the graphs of rational functions often have holes. Let’s review where those holes will occur at a zero of the denominator that is also a zero of the numerator. We should look for common factors between the numerator and denominator in factored form. A vertical asymptote will occur at the zero of the denominator that is not a zero of the numerator. We also find the horizontal asymptote, if it exists, using the fact above. Finally, sketch the graph.
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1. How do you find holes in a rational function?
2. What is the definition of a rational function?
3. How do you find Asymptotes?
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